A number of signal processing applications must find an inverse square root of a given positive-definite Hermitian matrix, K. For example, FIG. 1 is a schematic block diagram of an exemplary conventional multiple-input-multiple-output (MIMO) receiver system 100. A maximum likelihood detector 150 may be used for detecting signals sent via channels of this kind. Typically, when the MIMO channel is frequency-selective, a space-time equalizer 110 is used to pre-process the received signal to mitigate the spatial and temporal self-interference introduced by the channel. The space-time equalizer 110, however, spatially colors the Additive White Gaussian Noise (AWGN) at its input. Thus, the equalized signal is combined with colored noise. The non-white nature of this noise is known to impair the performance of the maximum likelihood detector 150.
Thus, a number of noise whiteners 130 have been proposed or suggested to perform “whitening” on the noise portion of the signal to remove the spatial correlation introduced by the space-time equalizer 110. Traditionally, noise whitening algorithms involve computing square roots and performing arithmetic division. The standard method for solving the inverse square root problem is based on Cholesky factorization. While algorithms based on Cholesky factorization work very well in software-based applications, they suffer from a number of limitations which make such algorithms unsuitable for a hardware implementation. Specifically, algorithms based on Cholesky factorization require scalar divisions and square roots which are computationally expensive operations to perform in hardware, due to their complexity.
A need therefore exists for a noise whitening algorithm that is suitable for a hardware implementation. A further need exists for an incremental noise whitening algorithm that only requires multiplication and addition operations. Yet another need exists for a method and apparatus for determining an inverse square root of a given positive-definite Hermitian matrix, K.